When I put my car in reversethe side view mirrors angle themselves downwards.
Then when I shift out of first the mirrors go back.

Is this a "feature" I didn't know I had (and also didn't know I needed)?

 

Only one at a time will tilt down. There's a toggle switch (L or R) which control your mirror adjustments. If this is in the middle setting - nothing happens when the car is in reverse. If it's moved to the L setting - the left mirror tilts when in reverse.

You'll wish you knew about it the first time you parallel park and scrape one side of your TL's rims on the curb.

 

It's in the manual and has been discussed many times. It is to assist with parallel parking. If you want to turn off this feature, move the side view mirror selector to the center position. If it is in the left position, the left mirror will tilt down, and if it is in the right position the right mirror will tilt down.

edit: Damn tripp...we must've been typing at the same time!